R Notebook

Projekt Dokumentation

Aufgabe: Vorhersage der Umsätze vom 9.6.2019 bis 30.07.2019

Infos zu den gegebenen Daten

Warengruppen: * 1 = Brot * 2 = Brötchen * 3 = Croissant * 4 = Konditorei * 5 = Kuchen * 6 = Saisonbrot

Saisonbrot muss nicht vorhergesagt werden! Siehe ‘predition_template.csv’.

Wetterdaten: * Mittlerer Bewölkungsgrad am Tag (0 = min, 8 = max) * MIttlere Temperatur in C * Mittlere Windgeschwindigkeit in m/s * Wettercode (http://www.seewetter-kiel.de/seewetter/daten_symbole.htm) * und in der Datei wettercodes.Rda

Vorbereitung & benötigte Libraries laden

remove(list = ls())
# Create list with needed libraries
pkgs <- c("lubridate", "stringr","tidyverse", "readr", 
          "fastDummies", "reticulate", "ggplot2", "Metrics", "VIM")

# Load each listed library and check if it is installed and install if necessary
for (pkg in pkgs) {
  if (!require(pkg, character.only = TRUE)) {
    install.packages(pkg)
    library(pkg, character.only = TRUE)
  }
}

Vorbereitete Datensätze laden

• Wetterdaten wurden in “Datenaufbereitung_Wetter.Rmd” vorbereitet
• Feiertagedaten wurden in “Datenaufbereitung_Feiertage.R” vorbereitet
• Schulferien wurden in “Datenaufbereitung_Schulferien.R” vorbereitet
• Umsatzdaten wurden in “Datenaufbereitung_Umsatz.R” vorbereitet

# Lade Daten
load("pj_wetter_dummy.Rda")
pj_wetter <- pj_wetter_dummy
  
load("kiwoDT.Rda")
pj_kiwo <- kiwoDT
  
load("pj_umsatz.Rda")

load("schulferien.Rda")
pj_schulferien <- schulferien

# Erste Betrachtung der Daten
#summary(pj_wetter)
#summary(pj_kiwo)
#summary(pj_umsatz)

allData_dummy

# Merge erstellt automatisch die Schnittmenge
# Der Zusatz all.x = TRUE sorgt dafür, dass keine Zeilen (basierend auf Datensatz x) weggelöscht werden
# Wetterdaten nach Datum hinzufügen
pj_umsatz_wetter <- merge(pj_umsatz, pj_wetter, by="Datum", all.x = TRUE)

# Schulferien nach Datum hinzufügen
pj_umsatz_wetter_ferien <- merge(pj_umsatz_wetter, pj_schulferien, by="Datum", all.x = TRUE)

# KiWo nach Datum hinzufügen
allData <- merge(pj_umsatz_wetter_ferien, pj_kiwo, by="Datum", all.x = TRUE)

# auf fehlende Werte überprüfen:
allData_na <- allData %>%
  aggr(combined=TRUE, numbers=TRUE)

Warning: not enough horizontal space to display frequencies

# Imputation Temperatur und Windstaerke
# Aktuell: "Datenspende" vom Wert vom Vortag
# ZIEL: Mittelwert aus Temperatur von Vortag und Tag danach -> Armando! :)
allData <- allData %>%  
  hotdeck(variable = c("Temperatur", "Windstaerke"),
          ord_var = "Datum")

#imputierte Werte graphisch überprüfen:
ggplot(allData) +
  geom_point(aes(x = Datum, y = Temperatur, color = Temperatur_imp))

ggplot(allData) +
  geom_point(aes(x = Datum, y = Windstaerke, color = Windstaerke_imp))

# NA Wettercodes zu 0, da Spalte WC_NA angibt, wo Wettercodes gefehlt haben
# Spalten 12 -24

# das gleiche gilt bei der Bewölkung
# Spalten 26 - 29

# weitere NA mit 0 füllen, dort wo es Sinn ergibt  

allData <- allData %>%
    mutate_at(c(12:34), ~replace(., is.na(.), 0))

# dummy coding der Wochentage
allData_dummy <- dummy_cols(allData, select_columns = "Wochentag")

allData_dummy$year <- year(allData_dummy$Datum)
allData_dummy$month <- month(allData_dummy$Datum)
allData_dummy$day <- day(allData_dummy$Datum)

allData_dummy$Datum <- NULL

summary(allData_dummy)

      Brot           Brötchen        Croissant        Konditorei         Kuchen         Saisonbrot    
 Min.   : 23.11   Min.   : 175.0   Min.   : 37.74   Min.   : 27.43   Min.   : 121.5   Min.   :  0.00  
 1st Qu.: 98.14   1st Qu.: 286.8   1st Qu.:106.79   1st Qu.: 66.12   1st Qu.: 231.1   1st Qu.:  0.00  
 Median :121.89   Median : 367.8   Median :143.90   Median : 79.67   Median : 268.2   Median :  0.00  
 Mean   :124.40   Mean   : 398.9   Mean   :164.52   Mean   : 87.12   Mean   : 278.2   Mean   : 11.02  
 3rd Qu.:147.06   3rd Qu.: 486.1   3rd Qu.:205.06   3rd Qu.: 97.41   3rd Qu.: 309.1   3rd Qu.:  0.00  
 Max.   :416.79   Max.   :1203.4   Max.   :565.94   Max.   :430.50   Max.   :1879.5   Max.   :172.87  
  Wochentag         Konditorei_imp   Windstaerke      Temperatur     WC_Bewölkung_abnehmend
 Length:2123        Mode :logical   Min.   : 2.00   Min.   :-8.475   Min.   :0             
 Class :character   FALSE:2069      1st Qu.: 5.00   1st Qu.: 6.312   1st Qu.:0             
 Mode  :character   TRUE :54        Median : 5.00   Median :11.650   Median :0             
                                    Mean   : 5.58   Mean   :12.031   Mean   :0             
                                    3rd Qu.: 6.00   3rd Qu.:17.769   3rd Qu.:0             
                                    Max.   :12.00   Max.   :32.671   Max.   :0             
 WC_Bewölkung_gleichbleibend WC_Bewölkung_nicht_beobachtet WC_Bewölkung_zunehmend WC_Dunst_Staub   
 Min.   :0                   Min.   :0.00000               Min.   :0.000000       Min.   :0.00000  
 1st Qu.:0                   1st Qu.:0.00000               1st Qu.:0.000000       1st Qu.:0.00000  
 Median :0                   Median :0.00000               Median :0.000000       Median :0.00000  
 Mean   :0                   Mean   :0.09279               Mean   :0.000471       Mean   :0.06924  
 3rd Qu.:0                   3rd Qu.:0.00000               3rd Qu.:0.000000       3rd Qu.:0.00000  
 Max.   :0                   Max.   :1.00000               Max.   :1.000000       Max.   :1.00000  
 WC_Ereignisse_letzte_h  WC_Gewitter      WC_Nebel_Eisnebel    WC_Regen        WC_Schauer   WC_Schnee      
 Min.   :0.0000         Min.   :0.00000   Min.   :0.00000   Min.   :0.0000   Min.   :0    Min.   :0.00000  
 1st Qu.:0.0000         1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0    1st Qu.:0.00000  
 Median :0.0000         Median :0.00000   Median :0.00000   Median :0.0000   Median :0    Median :0.00000  
 Mean   :0.1512         Mean   :0.01319   Mean   :0.01413   Mean   :0.3151   Mean   :0    Mean   :0.01978  
 3rd Qu.:0.0000         3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.:0    3rd Qu.:0.00000  
 Max.   :1.0000         Max.   :1.00000   Max.   :1.00000   Max.   :1.0000   Max.   :0    Max.   :1.00000  
 WC_Sprühregen      WC_Trockenereignisse     WC_NA        Bewoelkungsgrad_gering Bewoelkungsgrad_keine
 Min.   :0.000000   Min.   :0.00000      Min.   :0.0000   Min.   :0.0000         Min.   :0.00         
 1st Qu.:0.000000   1st Qu.:0.00000      1st Qu.:0.0000   1st Qu.:0.0000         1st Qu.:0.00         
 Median :0.000000   Median :0.00000      Median :0.0000   Median :0.0000         Median :0.00         
 Mean   :0.004239   Mean   :0.07772      Mean   :0.2346   Mean   :0.1182         Mean   :0.13         
 3rd Qu.:0.000000   3rd Qu.:0.00000      3rd Qu.:0.0000   3rd Qu.:0.0000         3rd Qu.:0.00         
 Max.   :1.000000   Max.   :1.00000      Max.   :1.0000   Max.   :1.0000         Max.   :1.00         
 Bewoelkungsgrad_mittel Bewoelkungsgrad_stark Bewoelkungsgrad_NA  Schulferien      KielerWoche    
 Min.   :0.0000         Min.   :0.0000        Min.   :0.000000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000         1st Qu.:0.0000        1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000         Median :0.0000        Median :0.000000   Median :0.0000   Median :0.0000  
 Mean   :0.3627         Mean   :0.3773        Mean   :0.004239   Mean   :0.2398   Mean   :0.0212  
 3rd Qu.:1.0000         3rd Qu.:1.0000        3rd Qu.:0.000000   3rd Qu.:0.0000   3rd Qu.:0.0000  
 Max.   :1.0000         Max.   :1.0000        Max.   :1.000000   Max.   :1.0000   Max.   :1.0000  
 Temperatur_imp     Windstaerke_imp    Wochentag_Friday Wochentag_Monday Wochentag_Saturday Wochentag_Sunday
 Min.   :0.000000   Min.   :0.000000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000     Min.   :0.0000  
 1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000     1st Qu.:0.0000  
 Median :0.000000   Median :0.000000   Median :0.0000   Median :0.0000   Median :0.0000     Median :0.0000  
 Mean   :0.007536   Mean   :0.007536   Mean   :0.1413   Mean   :0.1423   Mean   :0.1441     Mean   :0.1432  
 3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000     3rd Qu.:0.0000  
 Max.   :1.000000   Max.   :1.000000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000     Max.   :1.0000  
 Wochentag_Thursday Wochentag_Tuesday Wochentag_Wednesday      year          month            day      
 Min.   :0.0000     Min.   :0.0000    Min.   :0.0000      Min.   :2013   Min.   : 1.00   Min.   : 1.0  
 1st Qu.:0.0000     1st Qu.:0.0000    1st Qu.:0.0000      1st Qu.:2014   1st Qu.: 3.50   1st Qu.: 8.0  
 Median :0.0000     Median :0.0000    Median :0.0000      Median :2016   Median : 7.00   Median :16.0  
 Mean   :0.1432     Mean   :0.1432    Mean   :0.1427      Mean   :2016   Mean   : 6.52   Mean   :15.7  
 3rd Qu.:0.0000     3rd Qu.:0.0000    3rd Qu.:0.0000      3rd Qu.:2017   3rd Qu.:10.00   3rd Qu.:23.0  
 Max.   :1.0000     Max.   :1.0000    Max.   :1.0000      Max.   :2019   Max.   :12.00   Max.   :31.0  

save(allData_dummy, file="projectData_dummy.Rda")

Testdatensatz

# Erstelle einen leeren Dataframe mit einer Spalte für das Datum
testDatenSatz <- data.frame(Datum = character())

# Erstelle eine Sequenz von Daten im angegebenen Zeitraum
datum_sequenz <- seq(from = as.Date("2019-06-09"),
                     to = as.Date("2019-07-30"),
                     by = "days")

# Füge die Daten der Sequenz dem Dataframe hinzu
testDatenSatz <- rbind(testDatenSatz, data.frame(Datum = datum_sequenz))
testDatenSatz$Wochentag <- weekdays(testDatenSatz$Datum)
testDatenSatz <- merge(testDatenSatz, pj_wetter, by="Datum", all.x = TRUE)
testDatenSatz <- merge(testDatenSatz, pj_schulferien, by="Datum", all.x = TRUE)
testDatenSatz <- merge(testDatenSatz, pj_kiwo, by="Datum", all.x = TRUE)
### Testdatensatz ###

testDatenSatz <- testDatenSatz %>% 
  hotdeck(variable = c("Temperatur", "Windstaerke"),
          ord_var = "Datum")

#imputierte Werte von testDatenSatz graphisch überprüfen:
ggplot(testDatenSatz) +
  geom_point(aes(x = Datum, y = Temperatur, color = Temperatur_imp))

ggplot(testDatenSatz) +
  geom_point(aes(x = Datum, y = Windstaerke, color = Windstaerke_imp))

testDatenSatz <- testDatenSatz %>%
    mutate_at(c(4:26), ~replace(., is.na(.), 0))

# dummy coding der Wochentage
testDatenSatz <- dummy_cols(testDatenSatz, select_columns = "Wochentag")

testDatenSatz$year <- year(testDatenSatz$Datum)
testDatenSatz$month <- month(testDatenSatz$Datum)
testDatenSatz$day <- day(testDatenSatz$Datum)

testDatenSatz$Datum <- NULL

summary(testDatenSatz)

  Wochentag          Windstaerke      Temperatur    WC_Bewölkung_abnehmend WC_Bewölkung_gleichbleibend
 Length:52          Min.   :3.000   Min.   :14.46   Min.   :0              Min.   :0                  
 Class :character   1st Qu.:5.000   1st Qu.:16.93   1st Qu.:0              1st Qu.:0                  
 Mode  :character   Median :6.000   Median :19.59   Median :0              Median :0                  
                    Mean   :5.788   Mean   :20.41   Mean   :0              Mean   :0                  
                    3rd Qu.:7.000   3rd Qu.:23.40   3rd Qu.:0              3rd Qu.:0                  
                    Max.   :9.000   Max.   :29.73   Max.   :0              Max.   :0                  
 WC_Bewölkung_nicht_beobachtet WC_Bewölkung_zunehmend WC_Dunst_Staub   WC_Ereignisse_letzte_h  WC_Gewitter    
 Min.   :0.0000                Min.   :0              Min.   :0.0000   Min.   :0.0000         Min.   :0.0000  
 1st Qu.:0.0000                1st Qu.:0              1st Qu.:0.0000   1st Qu.:0.0000         1st Qu.:0.0000  
 Median :0.0000                Median :0              Median :0.0000   Median :0.0000         Median :0.0000  
 Mean   :0.1538                Mean   :0              Mean   :0.1346   Mean   :0.1538         Mean   :0.1154  
 3rd Qu.:0.0000                3rd Qu.:0              3rd Qu.:0.0000   3rd Qu.:0.0000         3rd Qu.:0.0000  
 Max.   :1.0000                Max.   :0              Max.   :1.0000   Max.   :1.0000         Max.   :1.0000  
 WC_Nebel_Eisnebel    WC_Regen        WC_Schauer   WC_Schnee WC_Sprühregen     WC_Trockenereignisse     WC_NA       
 Min.   :0         Min.   :0.0000   Min.   :0    Min.   :0   Min.   :0.00000   Min.   :0.00000      Min.   :0.0000  
 1st Qu.:0         1st Qu.:0.0000   1st Qu.:0    1st Qu.:0   1st Qu.:0.00000   1st Qu.:0.00000      1st Qu.:0.0000  
 Median :0         Median :0.0000   Median :0    Median :0   Median :0.00000   Median :0.00000      Median :0.0000  
 Mean   :0         Mean   :0.1731   Mean   :0    Mean   :0   Mean   :0.01923   Mean   :0.01923      Mean   :0.2308  
 3rd Qu.:0         3rd Qu.:0.0000   3rd Qu.:0    3rd Qu.:0   3rd Qu.:0.00000   3rd Qu.:0.00000      3rd Qu.:0.0000  
 Max.   :0         Max.   :1.0000   Max.   :0    Max.   :0   Max.   :1.00000   Max.   :1.00000      Max.   :1.0000  
 Bewoelkungsgrad_gering Bewoelkungsgrad_keine Bewoelkungsgrad_mittel Bewoelkungsgrad_stark Bewoelkungsgrad_NA
 Min.   :0.00000        Min.   :0.0000        Min.   :0.0000         Min.   :0.0000        Min.   :0         
 1st Qu.:0.00000        1st Qu.:0.0000        1st Qu.:0.0000         1st Qu.:0.0000        1st Qu.:0         
 Median :0.00000        Median :0.0000        Median :0.0000         Median :0.0000        Median :0         
 Mean   :0.05769        Mean   :0.1346        Mean   :0.4615         Mean   :0.3462        Mean   :0         
 3rd Qu.:0.00000        3rd Qu.:0.0000        3rd Qu.:1.0000         3rd Qu.:1.0000        3rd Qu.:0         
 Max.   :1.00000        Max.   :1.0000        Max.   :1.0000         Max.   :1.0000        Max.   :0         
  Schulferien      KielerWoche     Temperatur_imp Windstaerke_imp Wochentag_Friday Wochentag_Monday
 Min.   :0.0000   Min.   :0.0000   Min.   :0      Mode :logical   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0      FALSE:52        1st Qu.:0.0000   1st Qu.:0.0000  
 Median :1.0000   Median :0.0000   Median :0                      Median :0.0000   Median :0.0000  
 Mean   :0.5769   Mean   :0.1731   Mean   :0                      Mean   :0.1346   Mean   :0.1538  
 3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:0                      3rd Qu.:0.0000   3rd Qu.:0.0000  
 Max.   :1.0000   Max.   :1.0000   Max.   :0                      Max.   :1.0000   Max.   :1.0000  
 Wochentag_Saturday Wochentag_Sunday Wochentag_Thursday Wochentag_Tuesday Wochentag_Wednesday      year     
 Min.   :0.0000     Min.   :0.0000   Min.   :0.0000     Min.   :0.0000    Min.   :0.0000      Min.   :2019  
 1st Qu.:0.0000     1st Qu.:0.0000   1st Qu.:0.0000     1st Qu.:0.0000    1st Qu.:0.0000      1st Qu.:2019  
 Median :0.0000     Median :0.0000   Median :0.0000     Median :0.0000    Median :0.0000      Median :2019  
 Mean   :0.1346     Mean   :0.1538   Mean   :0.1346     Mean   :0.1538    Mean   :0.1346      Mean   :2019  
 3rd Qu.:0.0000     3rd Qu.:0.0000   3rd Qu.:0.0000     3rd Qu.:0.0000    3rd Qu.:0.0000      3rd Qu.:2019  
 Max.   :1.0000     Max.   :1.0000   Max.   :1.0000     Max.   :1.0000    Max.   :1.0000      Max.   :2019  
     month            day       
 Min.   :6.000   Min.   : 1.00  
 1st Qu.:6.000   1st Qu.:11.00  
 Median :7.000   Median :17.50  
 Mean   :6.577   Mean   :17.19  
 3rd Qu.:7.000   3rd Qu.:24.00  
 Max.   :7.000   Max.   :30.00  

save(testDatenSatz, file="Datenaufbereitung_Testdaten.Rda")

Features & Labels

features <- c("day",                           "month",                         "year",
              "Windstaerke",                   "Temperatur",                    "WC_Bewölkung_abnehmend",
              "WC_Bewölkung_gleichbleibend",   "WC_Bewölkung_nicht_beobachtet", "WC_Bewölkung_zunehmend",
              "WC_Dunst_Staub",                "WC_Ereignisse_letzte_h",        "WC_Gewitter",
              "WC_Nebel_Eisnebel",             "WC_Regen",                      "WC_Schauer",
              "WC_Schnee",                     "WC_Sprühregen",                 "WC_Trockenereignisse",
              "WC_NA",                         "Bewoelkungsgrad_gering",        "Bewoelkungsgrad_keine",
              "Bewoelkungsgrad_mittel",        "Bewoelkungsgrad_stark",         "Bewoelkungsgrad_NA",
              "Schulferien",                   "KielerWoche",                   "Wochentag_Tuesday",          
              "Wochentag_Thursday",
              "Wochentag_Friday",              "Wochentag_Wednesday",           "Wochentag_Monday",
              "Wochentag_Saturday",            "Wochentag_Sunday")

labels <- c("Brot", "Brötchen", "Croissant", "Konditorei", "Kuchen")

Selection of Training, Validation and Test Data

# Setting the random counter to a fixed value, so the random initialization stays the same (the random split is always the same)
set.seed(1)

assignment <- sample(1:2, size = nrow(allData_dummy), prob = c(.8, .2), replace = TRUE)

# Create training, validation and test data for the features and the labels
training_features <- allData_dummy[assignment == 1, features]    
training_labels <- allData_dummy[assignment == 1, labels]    
training_labels <- as.data.frame(training_labels)

validation_features <- allData_dummy[assignment == 2, features]  
validation_labels <- allData_dummy[assignment == 2, labels]  
validation_labels <- as.data.frame(validation_labels)

testing_features <- testDatenSatz %>% select(features)

#are there any missing values?
table(is.na(training_features))

FALSE 
55770 

table(is.na(validation_features))

FALSE 
14289 

table(is.na(testing_features))

FALSE 
 1716 

#summary(allData_dummy)

Modell aufstellen in Python

reticulate::repl_python()
import numpy as np
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import InputLayer, Dense, BatchNormalization, Dropout
from tensorflow.keras.optimizers import Adam

# The argument "input_shape" for the definition of the input layer must include 
# the number of input variables (features) used for the model. 
# To automatically calculate this number we use the function `r.training_features.keys()`, 
# which returns the list of variable names of the dataframe `training_features`.
# Then, the funtion `len()` returns the length of this list of variable names 
# (i.e. the number of variables in the input)

model = Sequential([
  InputLayer(input_shape = (len(r.training_features.keys()), )),
  BatchNormalization(),
  Dense(len(r.training_features.keys()), activation = 'swish'),
  Dropout(0.2),
  Dense(len(r.training_features.keys()), activation = 'swish'),
  Dropout(0.2),
  Dense(len(r.training_features.keys()), activation = 'swish'),
  Dense(5)
])

# Ausgabe einer ZUsammenfassung zur Form des MOdells, das geschätzt wird (nicht notwendig)
#model.summary()

Schätzung de neuronalen Netzes

# definition of the loss function and the optimazation function with hyperparameters
model.compile(loss="mape", optimizer=Adam(learning_rate=0.001))

#Schätzung des Modells
history = model.fit(r.training_features, r.training_labels, epochs = 250,
                    validation_data = (r.validation_features, r.validation_labels), verbose = 0)
                    
model.save("python_model.h5")

graphische Ausgabe der Modelloptimierung

quit
# Graphische Ausgabe der Modelloptimierung

#create data
data <- data.frame(val_loss = unlist(py$history$history$val_loss),
                   loss = unlist(py$history$history$loss))

ggplot(data[-(1:10), ])+
  geom_line(aes(x = 1:length(val_loss), y = val_loss, colour = "Validation Loss")) +
  geom_line(aes(x = 1:length(loss), y = loss, colour = "Training Loss")) +
  scale_colour_manual(values = c("Training Loss"="blue", "Validation Loss" = "red")) +
  labs(title = "Loss Function Values During Optimazation") +
  xlab("Iteration Number") +
  ylab("Loss")

Auswertung der Schätzergebnisse

# Schätzung der (normierten) Preise für die Trainings- und Testdaten
training_predictions <- py$model$predict(training_features)

 1/53 [..............................] - ETA: 1s
53/53 [==============================] - 0s 336us/step

validation_predictions <- py$model$predict(validation_features)

 1/14 [=>............................] - ETA: 0s
14/14 [==============================] - 0s 326us/step

testing_predictions <- py$model$predict(testing_features)

1/2 [==============>...............] - ETA: 0s
2/2 [==============================] - 0s 471us/step

# Vergleich der Gütekriterien für die Traingings- und Testdaten
a <- format(mape(training_labels[,1], training_predictions[,1])*100, digits=3, nsmall=2)
b <- format(mape(training_labels[,2], training_predictions[,2])*100, digits=3, nsmall=2)
c <- format(mape(training_labels[,3], training_predictions[,3])*100, digits=3, nsmall=2)
d <- format(mape(training_labels[,4], training_predictions[,4])*100, digits=3, nsmall=2)
e <- format(mape(training_labels[,5], training_predictions[,5])*100, digits=3, nsmall=2)

cat(paste0("\nMAPE on the Training Data1:\t", a))

MAPE on the Training Data1: 17.87

cat(paste0("\nMAPE on the Training Data2:\t", b))

MAPE on the Training Data2: 11.48

cat(paste0("\nMAPE on the Training Data3:\t", c))

MAPE on the Training Data3: 17.22

cat(paste0("\nMAPE on the Training Data4:\t", d))

MAPE on the Training Data4: 20.49

cat(paste0("\nMAPE on the Training Data5:\t", e, "\n"))

MAPE on the Training Data5: 13.37

g <- format(mape(validation_labels[,1], validation_predictions[,1])*100, digits=3, nsmall=2)
h <- format(mape(validation_labels[,2], validation_predictions[,2])*100, digits=3, nsmall=2)
i <- format(mape(validation_labels[,3], validation_predictions[,3])*100, digits=3, nsmall=2)
j <- format(mape(validation_labels[,4], validation_predictions[,4])*100, digits=3, nsmall=2)
k <- format(mape(validation_labels[,5], validation_predictions[,5])*100, digits=3, nsmall=2)
  
cat(paste0("\nMAPE on the Validation Data1:\t", g))

MAPE on the Validation Data1:   19.26

cat(paste0("\nMAPE on the Validation Data2:\t", h))

MAPE on the Validation Data2:   13.49

cat(paste0("\nMAPE on the Validation Data3:\t", i))

MAPE on the Validation Data3:   20.83

cat(paste0("\nMAPE on the Validation Data4:\t", j))

MAPE on the Validation Data4:   20.22

cat(paste0("\nMAPE on the Validation Data5:\t", k, "\n"))

MAPE on the Validation Data5:   14.42

# Mean of Training and Validation Data MAPE
meanT <- c(as.double(a), as.double(b), as.double(c), as.double(d), as.double(e)) 
meanV <- c(as.double(g), as.double(h), as.double(i), as.double(j), as.double(k)) 

cat(paste0("\nMean Training MAPE: ", mean(meanT), "\n"))

Mean Training MAPE: 16.086

cat(paste0("Mean Validation MAPE: ", mean(meanV), "\n"))

Mean Validation MAPE: 17.644

Grafischer vergleich der vorhergesagten & tatsächlicher Preise für die Trainings- und Validierungsdaten

data_train <- data.frame(prediction = training_predictions[,1], actual = training_labels[,1])
data_val <- data.frame(prediction = validation_predictions[,1], actual = validation_labels[,1])
data_test <- data.frame(prediction = testing_predictions[,1])

# Plot der Ergebnisse der Trainingsdaten
ggplot(data_train[]) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Training Data 1") +
  xlab("Case Number") +
  ylab("Price in EUR") 

# Plot der Ergebnisse der Validierungsdaten
ggplot(data_val[,]) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Validation Data 1") +
  xlab("Case Number") +
  ylab("Price in EUR")

# Plot der Ergebnisse der Testdaten
ggplot(data_test) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  labs(title="Prediction for the Test Data 1") +
  xlab("Case Number") +
  ylab("Price in EUR") 

#------------------------- 2 -------------------------#

data_train2 <- data.frame(prediction = training_predictions[,2], actual = training_labels[,2])
data_val2 <- data.frame(prediction = validation_predictions[,2], actual = validation_labels[,2])
data_test2 <- data.frame(prediction = testing_predictions[,2])

# Plot der Ergebnisse der Trainingsdaten
ggplot(data_train2) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Training Data 2") +
  xlab("Case Number") +
  ylab("Price in EUR") 

# Plot der Ergebnisse der Validierungsdaten
ggplot(data_val2) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Validation Data 2") +
  xlab("Case Number") +
  ylab("Price in EUR")

# Plot der Ergebnisse der Testdaten
ggplot(data_test2) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  labs(title="Prediction for the Test Data 2") +
  xlab("Case Number") +
  ylab("Price in EUR") 

#------------------------- 3 -------------------------#

data_train3 <- data.frame(prediction = training_predictions[,3], actual = training_labels[,3])
data_val3 <- data.frame(prediction = validation_predictions[,3], actual = validation_labels[,3])
data_test3 <- data.frame(prediction = testing_predictions[,3])

# Plot der Ergebnisse der Trainingsdaten
ggplot(data_train3) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Training Data 3") +
  xlab("Case Number") +
  ylab("Price in EUR") 

# Plot der Ergebnisse der Validierungsdaten
ggplot(data_val3) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Validation Data 3") +
  xlab("Case Number") +
  ylab("Price in EUR")

# Plot der Ergebnisse der Testdaten
ggplot(data_test3) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  labs(title="Prediction for the Test Data 3") +
  xlab("Case Number") +
  ylab("Price in EUR") 

#------------------------- 4 -------------------------#

data_train4 <- data.frame(prediction = training_predictions[,4], actual = training_labels[,4])
data_val4 <- data.frame(prediction = validation_predictions[,4], actual = validation_labels[,4])
data_test4 <- data.frame(prediction = testing_predictions[,4])

# Plot der Ergebnisse der Trainingsdaten
ggplot(data_train4) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Training Data 4") +
  xlab("Case Number") +
  ylab("Price in EUR") 

# Plot der Ergebnisse der Validierungsdaten
ggplot(data_val4) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Validation Data 4") +
  xlab("Case Number") +
  ylab("Price in EUR")

# Plot der Ergebnisse der Testdaten
ggplot(data_test4) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  labs(title="Prediction for the Test Data 4") +
  xlab("Case Number") +
  ylab("Price in EUR") 

#------------------------- 5 -------------------------#

data_train5 <- data.frame(prediction = training_predictions[,5], actual = training_labels[,5])
data_val5 <- data.frame(prediction = validation_predictions[,5], actual = validation_labels[,5])
data_test5 <- data.frame(prediction = testing_predictions[,5])

# Plot der Ergebnisse der Trainingsdaten
ggplot(data_train5) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Training Data 5") +
  xlab("Case Number") +
  ylab("Price in EUR") 

# Plot der Ergebnisse der Validierungsdaten
ggplot(data_val5) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  geom_line( aes(x=1:length(actual), y=actual, colour = "Actual Values" )) +
  scale_colour_manual( values = c("Predicted Values"="blue", "Actual Values"="red") ) +
  labs(title="Predicted and Actual Values for the Validation Data 5") +
  xlab("Case Number") +
  ylab("Price in EUR")

# Plot der Ergebnisse der Testdaten
ggplot(data_test5) +
  geom_line( aes(x=1:length(prediction), y=prediction, colour = "Predicted Values" )) +
  labs(title="Prediction for the Test Data 5") +
  xlab("Case Number") +
  ylab("Price in EUR")